This is a daily occurrence as I use StackExchange. Hit "Share..." Get the popup box, then struggle to select the entire URL.
While there may be iOS issues here, the point is the share textbox is intentionally too small to fit the URL.
And SE URLs are reasonably tinyfied, and of known size, which makes this undersizing rather senseless. It's like gating to exclude or frustrate mobile devices.
Here in iOS 9, you can drag the text box to the right, and it will even select invisible characters where they would be if the box were larger... Sometimes that works, but if you go 1px too far, it closes the selection area entirely and you must start over.
For my most copied URLs, I have taken to memorizing the last 3 digits of the URL and typing it in by hand.